Simplify to lowest terms. $\dfrac{18}{24}$
Solution: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 18 and 24? $18 = 2\cdot3\cdot3$ $24 = 2\cdot2\cdot2\cdot3$ $\mbox{GCD}(18, 24) = 2\cdot3 = 6$ $\dfrac{18}{24} = \dfrac{3 \cdot 6}{ 4\cdot 6}$ $\hphantom{\dfrac{18}{24}} = \dfrac{3}{4} \cdot \dfrac{6}{6}$ $\hphantom{\dfrac{18}{24}} = \dfrac{3}{4} \cdot 1$ $\hphantom{\dfrac{18}{24}} = \dfrac{3}{4}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{18}{24}= \dfrac{2\cdot9}{2\cdot12}= \dfrac{2\cdot 3\cdot3}{2\cdot 3\cdot4}= \dfrac{3}{4}$